9780130356826

0130356824

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Summary

This book bridges the gap between traditional algebra texts and reform texts, written to promote the AMATYC standards published as Crossroads in Mathematics. It provides users with a sound traditional mathematical foundation, fully integrates graphing calculator technology, and encourages computer activities. This book includes key topics in algebra such as linear equations and inequalities with one variable, systems of equations, polynomial functions and equations, quadratic functions and equations, exponential functions and equations, logarithmic functions an equations, and rational and radical expressions. For professionals who wish to brush up on their algebra skills or enhance them with the use of graphing calculators and computers.

Table of Contents

Preface

xi

Real Numbers

1

(94)

Rational Numbers and the Number Line

2

(13)

Addition and Subtraction

15

(13)

Multiplication and Division

28

(16)

Exponents and Roots

44

(16)

Scientific Notation

60

(10)

Properties of Real Numbers and Order of Operations

70

(25)

Chapter Summary

80

(1)

Section-by-Section Review

81

(8)

Chapter Review

89

(2)

Chapter Test

91

(2)

Chapter Project

93

(2)

Variables, Expressions, Equations, and Formulas

95

(48)

Variables and Algebraic Expressions

96

(7)

Simplifying Algebraic Expressions

103

(9)

Equations

112

(8)

Formulas

120

(23)

Chapter Summary

133

(1)

Section-by-Section Review

133

(4)

Chapter Review

137

(2)

Chapter Test

139

(1)

Chapter Project

140

(3)

Relations, Functions, and Graphs

143

(74)

Tables of Values, Ordered Pairs, and Relations

144

(11)

Rectangular Coordinate System and Graphing

155

(19)

Functions and Function Notation

174

(10)

Analyzing Graphs

184

(33)

Chapter Summary

200

(1)

Section-by-Section Review

200

(8)

Chapter Review

208

(2)

Chapter Test

210

(2)

Chapter Project

212

(2)

Chapter 1-3 Cumulative Review

214

(3)

Linear Equations in One Varible

217

(82)

Solving Equations Numerically and Graphically

218

(17)

Solving Equations by Using Addition and Multiplication

235

(11)

Solving Equations by Using a Combination of Properties

246

(12)

Solving Equations or Formulas for a Specified Variable

258

(8)

More Real-World Models

266

(10)

Solving Linear Absolute-Value Equations

276

(23)

Chapter Summary

286

(1)

Section-by-Section Review

286

(6)

Chapter Review

292

(2)

Chapter Test

294

(1)

Chapter Project

295

(4)

Linear Equations and Functions

299

(86)

Graphing by Using Ordered Pairs

300

(18)

Graphing by Using the Slope-Intercept Method

318

(22)

Coinciding, Parallel, and Perpendicular Lines

340

(11)

Writing Linear Equations from Given Data

351

(34)

Chapter Summary

367

(1)

Section-by-Section Review

368

(6)

Chapter Review

374

(3)

Chapter Test

377

(2)

Chapter Project

379

(3)

Chapter 1--5 Cumulative Review

382

(3)

Systems of Linear Equations

385

(76)

Solving Systems of Two Equations Graphically

386

(12)

Solving Systems of Two Equations by Using Substitution

398

(11)

Solving Systems of Two Equations by Using Elimination

409

(12)

More Real-World Models

421

(14)

Solving Systems of Linear Equations in Three Variables

435

(26)

Chapter Summary

448

(1)

Section-by-Section Review

448

(6)

Chapter Review

454

(2)

Chapter Test

456

(2)

Chapter Project

458

(3)

Linear Inequalities

461

(70)

Introduction to Linear Inequalities

462

(12)

Linear Inequalities in One Variable

474

(16)

Linear Inequalities in Two Variables

490

(15)

Systems of Linear Inequalities in Two Variables

505

(26)

Chapter Summary

517

(1)

Section-by-Section Review

518

(5)

Chapter Review

523

(2)

Chapter Test

525

(2)

Chapter Project

527

(1)

Chapter 1-7 Cumulative Review

528

(3)

Polynomial Functions

531

(62)

Introduction to Polynomials

532

(10)

Polynomial Functions and Their Graphs

542

(13)

Quadratic Functions and Their Graphs

555

(14)

Writing Quadratic Functions

569

(24)

Chapter Summary

571

(9)

Section-by-Section Review

580

(6)

Chapter Review

586

(2)

Chapter Test

588

(2)

Chapter Project

590

(3)

Exponents and Polynomials

593

(56)

Operations Involving Nonnegative Exponents

594

(12)

Operations Involving Negative Exponents

606

(8)

Polynomial Addition and Subtraction

614

(6)

Polynomial Multiplication

620

(10)

Polynomial Division

630

(19)

Chapter Summary

639

(1)

Section-by-Section Review

639

(4)

Chapter Review

643

(2)

Chapter Test

645

(1)

Chapter Project

646

(3)

Factoring

649

(58)

Greatest Common Factors

650

(12)

Factoring Perfect-Square Trinomials, Differences of Squares, and Sums and Differences of Cubes

662

(8)

Factoring Trinomials by Using the Trial-and-Error Method

670

(13)

Factoring Trinomials by Using the Grouping Method

683

(8)

General Strategies for Factoring

691

(16)

Chapter Summary

698

(1)

Section-by-Section Review

699

(3)

Chapter Review

702

(1)

Chapter Test

703

(1)

Chapter Project

704

(3)

Quadratic and Other Polynomial Equations and Inequalities

707

(92)

Solving Equations Numerically and Graphically

708

(11)

Solving Equations Algebraically by Factoring

719

(10)

Solving Quadratic Equations by Using Square Roots

729

(12)

Solving Quadratic Equations by Completing the Square

741

(8)

Solving Quadratic Equations by Using the Quadratic Formula

749

(12)

More Real-World Models

761

(8)

Solving Quadratic Inequalities

769

(30)

Chapter Summary

784

(1)

Section-by-Section Review

784

(7)

Chapter Review

791

(2)

Chapter Test

793

(1)

Chapter Project

794

(3)

Chapters 1--11 Cumulative Review

797

(2)

Rational Expressions, Functions, and Equations

799

(78)

Rational Expressions and Functions

800

(15)

Multiplication and Division of Rational Expressions

815

(12)

Addition and Substraction of Rational Expressions

827

(16)

Solving Rational Equations in One Variable

843

(12)

More Real-World Models

855

(22)

Chapter Summary

865

(1)

Section-by-Section Review

865

(6)

Chapter Review

871

(2)

Chapter Test

873

(1)

Chapter Project

874

(3)

Radical Expressions, Functions, and Equations

877

(96)

Radical Expressions, Functions, and Graphs

878

(13)

Rational Exponents

891

(11)

Properties of Rational Exponents

902

(7)

Properties of Radicals

909

(11)

Operations on Radicals

920

(8)

Solving Radical Equations in One Variable

928

(12)

Equations with Imaginary-Number Solutions

940

(33)

Chapter Summary

956

(1)

Section-by-Section Review

957

(7)

Chapter Review

964

(2)

Chapter Test

966

(2)

Chapter Project

968

(2)

Chapter 1--13 Cumulative Review

970

(3)

Exponential and Logarthmic Functions and Equations

973

(67)

Inverse Functions

974

(12)

Exponential Functions

986

(11)

Logarithmic Functions

997

(13)

Properties of Logarithms

1010

(6)

Solving Exponential and Logarithmic Equations

1016

(24)

Chapter Summary

1027

(1)

Section-by-Section Review

1027

(6)

Chapter Review

1033

(2)

Chapter Test

1035

(1)

Chapter Project

1036

(2)

Chapter 1--14 Cumulative Review

1038

(2)

Photo Credits

1040

Selected Answers

1

(1)

Index

1

Excerpts

The second edition ofExperiencing Introductory and Intermediate Algebracontinues to embrace the goal of promoting a new approach to teaching and learning developmental mathematics. This approach combines a traditional model with the reform movements presented in the National Council of Teachers of Mathematics (NCTM) standards and the American Mathematical Association of Two-Year Colleges (AMATYC) standards. The NCTM goals state that in our present technological society, students should learn to value mathematics, reason and communicate mathematically, become confident of their mathematical abilities, and become mathematical problem solvers. The AMATYC standards for intellectual development state that students will model real-world situations, connect mathematics with other disciplines, and use appropriate technology. In this second edition, we have incorporated recommendations and suggestions from instructors and reviewers of the text. Instructors who currently use the text valued the real-world application feature and encouraged us to expand it. At the same time, they recommended that the text be streamlined to reduce its volume. The contents of this edition are still organized by families of functions, according to the AMATYC standards. Consequently, the first seven chapters of the text focus on linear expressions, equations, and functions. The next four chapters, Chapters 8 through 11, focus on polynomial expressions, equations, and functions. Chapter 12 presents rational expressions, equations, and functions, Chapter 13 examines radical expressions, equations, and functions, and Chapter 14 features exponential and logarithmic expressions, equations, and functions. We have condensed the discussion of the real-number system into a review of pre-algebra numeric topics that may be taught as a whole or by sections of choice. We have combined Chapters 1 and 2 of the previous edition into one chapter, postponing the discussion of rational exponents to a later chapter. Also, the coverage of radicals in the combined chapter is limited to square roots and cube roots. In the previous edition, exponents and polynomials were presented together with factoring, all within one chapter. We have now separated this material into two chapters. The first of the two, Chapter 9, focuses on exponents and polynomial operations. We have added a separate section on polynomial division that outlines polynomial long division in greater detail. Feedback from reviewers indicated a need for expanding and strengthening the discussion of factoring, so we have created a separate chapter on the subject, Chapter 10. In this new chapter, we offer more examples, more exercises, and a different ordering of topics. In the previous edition, there was a separate chapter on complex numbers. In this edition, complex numbers and equations with imaginary solutions have been placed at the end of Chapter 13, following the discussion of radical expressions, equations, and functions. We believe that that is the appropriate place for complex numbers for two major reasons: students will have just learned the algebra of radicals, and the new location provides a perfect opportunity to revisit the quadratic formula, thereby reinforcing their understanding of the concept. However, the section on complex numbers and equations with imaginary solutions has been written as a stand-alone section, and if an instructor so chooses, it could be presented after the discussion of the quadratic formula in Chapter 11. The first half of the text presents a balanced discussion of algebraic, numerical, and graphical methods for solving linear equations, so that students have a solid understanding of what the concepts represent. In the second half, the discussion of polynomial equations continues to utilize the same algebraic, numerical, and graphical techniques. This approach provides an opportunity for students who enter the sequence at that late point t